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If a, b, and c are three different positive. . .

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by Vincen » Fri Sep 29, 2017 7:03 pm
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c

The OA is A.

How can I prove that option A is the correct choice?
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by GMATGuruNY » Sat Sep 30, 2017 3:09 am
Vincen wrote:If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c

The OA is A.

How can I prove that option A is the correct choice?
If a=5, b=11 and c=13, then all 3 values are prime, as is their sum:
5+11+13 = 29.

Thus, option A could be true.

The correct answer is A.
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Re: If a, b, and c are three different positive. . .

by Scott@TargetTestPrep » Wed Jan 29, 2020 5:20 am
Vincen wrote: ↑
Fri Sep 29, 2017 7:03 pm
 If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c

The OA is A.

How can I prove that option A is the correct choice?
We can let a, b, and c be 5, 7, and 11, respectively. We see that 5 + 7 + 11 = 23 is prime, and each of a, b, and c is also a prime.

Answer: A

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